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{"sheet":"2 by 2","index":0,"n_rows":35,"n_cols":9,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
[null," Systems of Linear Equations"]
[]
[null,null,"This spreadsheet uses "]
[null,null,"         matrix methods"]
[null,null,"      to solve systems of"]
[null,"   two linear equations in two unknowns"]
[]
[]
["First enter the values for the matrix of coefficients A in AX = B:  "]
[]
[null,null,1,1]
[null,null,2,3]
[null,null,null,null,null,null,{"$f":"IF(MDETERM($C$11:$D$12)=0,\"\",\"The solution matrix X is\")","v":"The solution matrix X is"}]
[]
["Enter the values for the matrix of constants B in AX = B:  ",null,null,null,null,null,null,"x =",{"$f":"IF(MDETERM(C11:D12)=0,\"\",Sheet4!A1)","v":1}]
[null,null,null,null,null,null,null,"y =",{"$f":"IF(MDETERM(C11:D12)=0,\"\",Sheet4!A2)","v":4}]
[null,null,5]
[null,null,14]
[]
[]
[{"$f":"IF(MDETERM($C$11:$D$12)=0,\"This matrix of coefficients does not have an inverse\",\"\")","v":""}]
[{"$f":"IF(MDETERM(C11:D12)=0,\"    So the system of equations does not have a solution\",\"\")","v":""}]
["Click each item below for suggestions and investigations"]
[null,"   Item 1"]
[null,"   Item 2"]
[null,"   Item 3"]
[]
[]
[]
[]
["Created by:  Sheldon P. Gordon"]
["                     Farmingdale StateCollege"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"3 by 3","index":1,"n_rows":27,"n_cols":10,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
[null," Systems of Linear Equations"]
[]
[null,null,"This spreadsheet uses "]
[null,null,"         matrix methods"]
[null,null,"      to solve systems of"]
[null,"     three linear equations in three unknowns"]
[]
[]
["First enter the values for the matrix of coefficients A in AX = B:  "]
[]
[null,null,1,3,-2]
[null,"A =",2,7,5]
[null,null,-1,4,7,null,null,{"$f":"IF(MDETERM($C$11:$D$12)=0,\"\",\"The solution matrix is\")","v":"The solution matrix is"}]
[]
["Enter the values for the matrix of constants B in AX = B:  ",null,null,null,null,null,null,null,"x =",{"$f":"IF(MDETERM(C11:E13)=0,\"\",Sheet4!C1)","v":-5.5}]
[null,null,null,null,null,null,null,null,"y =",{"$f":"IF(MDETERM(C11:E13)=0,\"\",Sheet4!C2)","v":1.8448275862068966}]
[null,null,2,null,null,null,null,null,"z =",{"$f":"IF(MDETERM(C11:E13)=0,\"\",Sheet4!C3)","v":-0.98275862068965525}]
[null,"B =",-3]
[null,null,6]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,"   Item 1"]
[null,"   Item 2"]
[null,"   Item 3"]

{"sheet":"4 by 4","index":2,"n_rows":30,"n_cols":11,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
[null," Systems of Linear Equations"]
[]
[null,null,"This spreadsheet uses "]
[null,null,"         matrix methods"]
[null,null,"      to solve systems of"]
[null,"    four linear equations in four unknowns"]
[]
[]
["First enter the values for the matrix of coefficients A in AX = B:  "]
[]
[null,null,1,3,0,-2]
[null,"A =",2,7,3,5]
[null,null,3,-4,-5,3]
[null,null,0,4,8,-5,null,null,{"$f":"IF(MDETERM($C$11:$D$12)=0,\"\",\"The solution matrix is\")","v":"The solution matrix is"}]
[]
["Enter the values for the matrix of constants B in AX = B:  ",null,null,null,null,null,null,null,null,"x1 =",{"$f":"IF(MDETERM(C11:F14)=0,\"\",Sheet4!E1)","v":0.46966292134831444}]
[null,null,null,null,null,null,null,null,null,"x2 =",{"$f":"IF(MDETERM(C11:F14)=0,\"\",Sheet4!E2)","v":0.44719101123595517}]
[null,null,2,null,null,null,null,null,null,"x3 =",{"$f":"IF(MDETERM(C11:F14)=0,\"\",Sheet4!E3)","v":0.46741573033707862}]
[null,null,5,null,null,null,null,null,null,"x4 =",{"$f":"IF(MDETERM(C11:F14)=0,\"\",Sheet4!E4)","v":-9.4382022471910132E-2}]
[null,"B =",-3]
[null,null,6]
[]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,"   Item 1"]
[null,"   Item 2"]
[null,"   Item 3"]

{"sheet":"Sheet4","index":3,"n_rows":4,"n_cols":5,"rows_kept":4,"cut":false,"hidden":false,"merged":[]}
[{"$f":"MMULT(MINVERSE('2 by 2'!C11:D12),'2 by 2'!C17:C18)","v":1},null,{"$f":"MMULT(MINVERSE('3 by 3'!C11:E13),'3 by 3'!C17:C19)","v":-5.5},null,{"$f":"MMULT(MINVERSE('4 by 4'!C11:F14),'4 by 4'!C18:C21)","v":0.46966292134831444}]
[4,null,1.8448275862068966,null,0.44719101123595517]
[null,null,-0.98275862068965525,null,0.46741573033707862]
[null,null,null,null,-9.4382022471910132E-2]